For this approach to confidence intervals, the sample is assumed to be representative of the population. We draw 10,000 samples -- called bootstrap samples -- from the original sample with replacement. This simulates sampling from a sufficiently large population which has the same characteristics as the given sample. For each bootstrap sample, we calculate a mean, proportion, or difference. The bounds of the confidence interval are then found using percentiles of these 10,000 values. For each interval, we draw a histogram of the 10,000 values. In the histograms:

• Red lines indicate the bounds of the confidence interval.
• Green either indicates original data values or the statistic from the original sample.
• For differences, a blue line indicates the location of 0.

In these tests, an ideal population is created satisfying the null hypothesis. Then 10,000 samples are drawn from the ideal population, and a test statistic is computed for each sample. The P-value is the proportion of the samples with test statistics as extreme as the original. Each test gives a histogram indicating the test statistics for the 10,000 samples. The original test statistic is displayed in green, and the extreme test statistics are displayed in red.

The test statistics used are: